Pathwise integrals and Ito-Tanaka Formula for Gaussian processes

We prove the Ito-Tanaka formula and the existence of pathwise stochastic integrals for a wide class of Gaussian processes. Motivated by financial applications, we define the stochastic integrals as forward-type pathwise integrals introduced by F\"ollmer and as pathwise generalized Lebesgue-Stieltjes integrals introduced by Z\"ahle. As an application, we illustrate the importance of Ito-Tanaka formula for pricing and hedging of financial derivatives.